In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line `x+y=2` touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = `6sqrt2` units. The equation of the pair of asymptotes isA. `5xy+2x^(2)+2y^(2)=0`B. `3x^(2)+4y^(2)+6xy=0`C. `2x^(2)+2y^(2)-5xy=0`D. none of these

In a hyperbola, the portion of the tangent intercepted between the asy

1.	In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line `x+y=2` touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = `6sqrt2` units. The equation of the pair of asymptotes isA. `5xy+2x^(2)+2y^(2)=0`B. `3x^(2)+4y^(2)+6xy=0`C. `2x^(2)+2y^(2)-5xy=0`D. none of these
Answer» Correct Answer - A The equation of tangent in parametric form is given by `(x-1)/(-1//sqrt2)=(y-1)/(1//sqrt2)= pm3sqrt2` `"or "A-=(4,-2), B-=(-2,4)` The equation of asymptotes (OA and OB) are given by `y+2=(-2)/(4)(x-4)` `"or "2y+x=0` `"and "y-4=(4)/(-2)(x+2)` `"or "2x+y=0` Hence, the combined equation of asymptotes is `(2x+y)(x+2y)=0` `"or "2x^(2)+2y^(2)+5xy=0`

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